import numpy as np
import matplotlib.pylab as plt
def numGrad(f, x):
h = 1e-4 # 0.0001
grad = np.zeros_like(x)
for idx in range(x.size):
tmp_val = x[idx]
x[idx] = float(tmp_val) + h
fxhP = f(x) # f(x+h)
x[idx] = tmp_val - h
fxhM = f(x) # f(x-h)
grad[idx] = (fxhP - fxhM) / (2*h)
x[idx] = tmp_val # 値を元に戻す
return grad
def gradDesc(f, init_x, lr=0.01, step_num=100):
x = init_x
x_history = []
for i in range(step_num):
x_history.append( x.copy() )
grad = numGrad(f, x)
x -= lr * grad
return x, np.array(x_history)
def function_2(x):
return (x[0]**2)/20 + x[1]**2
init_x = np.array([-3.0, 4.0])
lr = 0.9
step_num = 100
x, x_history = gradDesc(function_2, init_x, lr=lr, step_num=step_num)
plt.plot( [-5, 5], [0,0], '--b')
plt.plot( [0,0], [-5, 5], '--b')
plt.plot(x_history[:,0], x_history[:,1], '-o')
plt.xlim(-3.5, 3.5)
plt.ylim(-4.5, 4.5)
plt.xlabel("X0")
plt.ylabel("X1")
plt.show()

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